Predicting What Comes Next: Exploring Sequences and Progressions Mind Map

A sequence is an ordered list of numbers, objects, or quantities written according to a rule or pattern.

Always write the term position along with the term value when solving missing-term or nth-term questions.

An explicit rule gives the value of any term directly using its position number n.

Before substituting, write what n means: n = required position number.

A recursive rule defines each term of a sequence using one or more previous terms, along with a starting term.

In recursive questions, mention both the first term and the rule for getting the next term.

An arithmetic progression is a sequence in which the difference between every two consecutive terms is constant.

Check at least two consecutive differences before calling a sequence an AP.

The sum of the first n terms of an arithmetic progression is the total obtained by adding its first n terms.

Choose Sn = n/2 × (a + l) only when the last required term l is known or can be found correctly.

A geometric progression is a sequence in which each term is obtained by multiplying the previous term by the same non-zero constant ratio.

To test a GP, divide consecutive terms: second by first, third by second, and so on.

Real-world applications of sequences use ordered patterns to model repeated changes in money, distance, growth, decay, arrangements, or daily-life quantities.

Underline the phrase showing change: fixed increase suggests AP; multiplied by the same factor suggests GP.